"Save the cat" is a term coined by the late
Blake Snyder in manual of screenwriting of the same name. And while it was
created for the purposes of screenwriting I feel that it works just as a well
for a longer work of fiction.
The term is used to describe the scene where the
audience (or reader) first meets the protagonist. The idea is that the
character has to do something nice to make the hero like the character and
begin to sympathize with them- that it is important to make the reader's first
impression of the protagonist a positive one.
The term incidentally comes from the opening scene of
Alien, where the hero Ridley saves a cat named Jones.
This technique also helps to insulate the character
from backlash later on if that person makes a decision that is morally
questionable, arrogant, or even downright evil. The initial impression is
supposed to linger and the audience remembers that the protagonist is not all
bad, because he saved the cat.
I recently did an experiment where I wrote two similar
short pieces where the main character is attempting to escape from a sinking
ship. In one I had him furiously attempting to escape as fast as he could. In
the second the only difference was that I had him attempt to save the life of a
person who was on the verge of death by carrying him, thus slowing him down.
Overwhelmingly people preferred the version where the
hero saves the cat. I know this is just anecdotal evidence, but I'm convinced.